Accuracy of the EGSnrc Monte Carlo Code System

1/47
Accuracy of the EGSnrc code system
D. W. O. Rogers,
Carleton Laboratory for
Radiotherapy Physics,
Physics Dept,
Carleton University,
Ottawa
http://physics.carleton.ca/~drogers
ICCR Melbourne Australia May 9, 2013

2/47
Accuracy and Limitations of EGSnrc
• Fano test
• real ion chambers
• k Q calculations
• multiple scattering tests
• backscatter data for x-rays and megavoltage
• transmission test of extreme conditions
• brachytherapy spectra and dose rate constants

3/47
How accurately can we calculate ion
chamber response? The Fano test
Fano’s theorem
Under conditions of charged particle equilibrium the
electron fluence in a medium is independent of the
density.
Fano cavity chamber,
- full build up wall
- cavity either: gas of wall material or wall material
- perfect CPE => no attenuation or scattered photons

4/47
Fano test (cont)
Consider the case with cavity of wall material
but since, by Fano’s theorem the electron fluence
is unchanged =>
and hence:
where D gas is the dose to the gas without any
attenuation and scatter (so there is CPE) and D’ gas
is the dose calculated with attenuation and scatter
and then corrected by the wall correction factor,
i.e. K wall (not another kerma!)

Fano test (cont)
-cover of
EGSnrc
manual
-against own
cross sections
60
Co
-ESTEPE is
max fractional
step size
This is the toughest test I know for any
electron-photon Monte Carlo code
5/47

Fano test (cont)
• with lead walls, EGSnrc passes at 0.1 % level in
60
Co (La Russa, Med Phys 35(2008) 5629).
– No parameter adjustment needed
-
- Sempau and Andreo (PMB, 51 (2006) 3533-3548)
achieved similar accuracy with PENELOPE (used
different version of Fano test) as did Yi et al
(Med Phys 33 (2006) 1213)
- both cases needed adjustment of parameters
- Poon et al (PMB 50 (2005) 681 - 694) showed that
GEANT4 failed Fano test by as much as 39%.
- now within 1% at expense of long CPU times
(Sawakuchi, private communication)
6/47

7/47
Fano test (cont)
• the Fano test assesses accuracy against its own
cross sections.
– If cross sections are wrong, test can still be
passed if mass energy absorption coefficients
are calculated with same cross sections.
• real test is against measured ion chamber data.

eal chambers in 60 Co beams
1958
1957
1954
1992
2007
La Russa & Rogers Med Phys 35 (2008) 5629-5640
8/47

Whyte: variation of pressure/wall
• Co-60 beam
• data normalized
only once
•i.e. relative
values are
meaningful
•depends on
cross sections
• RMSD = 0.5%
Med Phys 35 (2008) 5629-5640
9/47

Nilsson et al: wall variations
• 60 Co
•normalized to
polystyrene
chamber
•RMSD=1.4%
(EGSnrc/expt)
•depends on
cross-sections
Med Phys 35 (2008) 5629-5640
10/47

What affects the calculation?
against
measured
data
Kawrakow & Rogers, MC2000, p135 based on data of
Nilsson et al, Med Phys 19(1992)1413
11/47

Burns: variation of graphite chamber
• 60 Co
• RMSD = 0.03%
• (0.7% overall
variation)
La Russa Med Phys 35 (2008) 5629-5640
12/47

13/47
Response vs angle of pancake chamber
R/A wall should be
constant.
It is, within 0.3%
despite 8%
variation.
(residual 0.3% is a
K an effect)
McCaffrey et al PMB 49(2004) 2491

14/47
ab initio Monte Carlo calculations of
k Q for clinical ion chambers
• Fano test is usually for simple `in air’ ion chambers
• real interest is `in-phantom’
• egs_chamber code of Wulff et al (Med Phys 35
(2008) 1328)
– very efficient: correlated sampling
– handles complex realistic geometries
A12
NE2571

15/47
Calculating k Q (protocol clinical
dosimetry)
• definitions:
assume (W/e)
is independent
of beam
quality

16/47
9 different “classes” of detectors
black:TG51
gold: fit
labels:(wall/
electrode)
Note large
effects of
high-Z
electrodes

17/47
Uncertainties on calculated k Q
• EGSnrc is accurate to 0.1 % against its own cross sections
• what are effects of cross section uncertainties?
– are they correlated or not?
• probably correlated for megavoltage photons
• what is uncertainty on (W/e) air being constant?
– TRS-398 says 0.5% but evidence for any value is very
thin

18/47
Cross section uncertainties on k Q
standard error propagation, assuming uncorrelated
where u(x i ) is the uncertainty on cross section x i
Approximate
where
is change in k Q when i-th cross section is
changed by .
Calculate for a corresponding to u(x i ).

Uncertainties on k Q for all chambers
correlated or uncorrelated
worst case: 0.39% 0.86% 0.63% 0.99%
Muir & Rogers Med Phys 37 (2010) 5939
19/47

Experimental measurements of k Q
• many measurements done, but most papers
measure one or two types of chambers
• McEwen measured k Q for 27 different types
against the Canadian primary standards of
absorbed dose using ---->
(Med. Phys. 37 (2010) 2179)
• for “well-behaved” chambers
measurement uncertainty on k Q was 0.30%
• agreement with TG—51 values is excellent,
typically 0.5% or better for “well-behaved”
20/47

Consistency of measured k Q
diamonds are
from standards
labs (Stucki et
al, to be
published)
0.3%
NE2571
Muir et al Med Phys 38 (2011) 4600
21/47

How well do calculations and
measurements agree?
For 26 chambers in common,
-χ 2 /df < 0.65 for all chambers at 1 energy
- χ
2 /df < 1 for all chambers vs energy except 1
Suggests, if anything, uncertainties are too large
http://www.physics.carleton.ca/clrp/kQ
22/47

23/47
Measured vs calculated k Q
26 chambers
in common
shaded part is
less precise
chambers
remarkable
agreement

24/47
Backscatter coefficients
• e - backscatter is the most difficult physical quantity
for Monte Carlo to calculate
– unfortunately it is also hard to measure accurately
• it is defined as the number of e- reflected from a
surface per incident e- (above a low energy cutoff,
about 50 eV to exclude secondary electron emission
from the surface)

Backscatter - a tough test: kilovolts
experimental data scatter about calculated values
Ali & Rogers PMB 53(2008) 1527-1543
25/47

Backscatter - spectra
Ali & Rogers J Phys D: App Phys 41 (2008)055505
26/47

27/47
Backscatter: megavolts
Ali et al, in preparation

Accuracy of multiple scattering
Multiple scattering is a dominant physical effect for e-
EGSnrc uses a multiple scattering theory developed by
Kawrakow (NIMB 134 (1998) 325-336)
It has the advantage of seamlessly converting into a
single scattering theory for very short steps.
Recently there have been some high quality
measurements done by my ex-colleagues at NRC to test
the theory as implemented in EGSnrc
Ross et al, Med Phys 35 (2008)4121 - 4131
i
28/47

NRC experimental setup
Med Phys 35 (2008)4121 - 4131
29/47

NRC’s results
symbols: expt
lines: EGSnrc
symbols: expt
lines: EGSnrc
Note the experiment is slightly wider than calculations
Thanks to Malcolm McEwen for the raw data
Med Phys 35 (2008) 4121 - 4131
30/47

NRC’s results for q 1/e widths
Experimental
uncertainty
about 1 %.
each bar is a measurement with a different thickness foil
Ross et al Med Phys 35 (2008) 4121 - 4131
31/47

Transmission analysis
e -
target
collimator
attenuator
collimator
detector
Goal of project was accurate determination of brem spectra
from linac beams. Also provides a very stringent benchmark.
Ali et al Med. Phys. 39 (2012) 5990
32/47

33/47
Attenuator rack
graphite
lead

Uncertainty budget on T(d,x i )
• 10 MV much worse since low energy limit of machine
• take into account
– short term drifts < 0.15% P pol < 0.15%
– leakage < 0.1% P ion < 0.03%
– Monitor stability 0.1%
– attenuator thickness

35/47
A problem
• the calculated transmission was wrong by up to 7%
compared to the 0.64% experimental measurements.
• attenuation by a factor of 100 is very sensitive to
errors in cross section.
– consider a monoenergetic case
• T=0.01 => e -mx = 0.01 but say m should be 1.01m
and hence T = e -1.01mx = (e -mx ) 1.01 = 0.095
i.e. a 1% error causes a 5% change in T
• what about photonuclear interactions?

36/47
photonuclear cross sections
(γ,n) + (γ,p)
from E Ali
PhD thesis

Effects of photonuclear interactions
Ali added
photonuclear
attenuation
(no energy
deposition) into
EGSnrc
case shown is
worst case since
high energy
analytic vs Monte Carlo as check on implementation
37/47

Aside: photonuclear effects on a
clinical spectrum
from E Ali (unpublished)
38/47

Direct comparisons of transmission data
Symbols
different
target/energy
combinations.
x is 10 MV/Al
0.4% cross
section change
can explain all
discrepancies
within
uncertainties.
Do data tie down uncertainties on Xsections?
39/47

40/47
Calculation vs measurement
(ratios of T different targets,detectors,attenuators)
remarkable
agreement
uncertainties
from photon
cross sections
drop out of
ratios (same in
both)

41/47
Transmission: a very tough benchmark for
Monte Carlo codes
• these data are a very stringent test of any MC
code system
– had to re-engineer XCOM cross sections
– add photonuclear attenuation
– use KM brem angular sampling rather than
“simple” option in EGSnrc
• there is a report with all the data required to do a
detailed comparison with Geant4, PENELOPE,
MCNP.

42/47
Brachytherapy benchmarks
• Monte Carlo plays an essential role in brachytherapy
dosimetry
– calculates TG-43 parameters such as g(r), F(r,q),
L (dose rate constant)
• very hard to confirm these calculations with much
accuracy as experiments have large uncertainties (5%).
• there have been teams measure spectra from multiple
seeds with reasonable consistency

125
I spectra (calculated)
based on Rodriguez Med Phys 40(2013) 011713
43/47

Calculated vs measured branching ratios
Agreement
about same
as variations
in expt.
0.264 0.071 1.0 0.250 0.068
0.260 0.069 1.0 0.249 0.0675
Same for 20
seeds total
0.0 0.0 1.0 0.250 0.068
Rodriguez and Rogers Med Phys 40(2013) 011713
44/47

What about measured vs calculated dose
rate constants?
• TG-43 and its updates recommend averaging
calculated and measured values of L
• this is because there is a systematic difference
between them of 4.6% for 125 I as published.
• Problems:
– intrinsic energy dependence of the TLDs used in
the measurements was not properly accounted
for (an 8.2% effect relative to 60 Co)
– relative absorbed dose energy dependence of
the different sizes of TLD chips used needed to
be accounted for (a 2.7% effect)
• properly accounting for these, average difference
for 22 measurements for 17 seeds drops to 0.8%
45/47

46/47
Conclusions
• The EGSnrc code system is capable of accurately
simulating a wide variety of experimental
benchmarks
• By testing any computer code system we
constantly are forced to make improvements
– e.g. adding photonuclear attenuation and
reworking the use of the XCOM cross sections

47/47
Thank you for your attention
• much of the work was done by students and colleagues
– Elsayed Ali, Bryan Muir, Dan La Russa, Manuel
Rodriguez and Rowan Thomson at Carleton University
– the k Q experiments were in conjunction with NRC’s
Malcolm McEwen
– EGSnrc and BEAMnrc systems have been developed
and maintained by colleagues at NRC over the years
• Iwan Kawrakow, Ernesto Mainegra-Hing,
Blake Walters, Frederic Tessier
-work supported by a Vanier Scholarship, and NSERC CGS,
OGSSTs, the CRC program, an NSERC DG, CFI and OIT

em yield from thick targets
Faddegon et al Med Phys 17 (1990) 773 and
Med Phys 18 (1991) 727
measured brem yield as a function of energy and angle
for many different target materials and compared their
results to EGS4 calculations.
Typical experimental uncertainty: 5%
Faddegon et al Med Phys 35(2008) 4308 compared same
measured data to 3 Monte Carlo codes:
EGSnrc, GEANT4 and PENELOPE
48/47

em total yield vs incident energy
thick targets
5% uncertainty
on
measurements
photons
> 220 keV
Faddegon et al Med Phys 35 (2008) 4308
49/47

em yield vs angle at 15 MV
thick
targets
photons
> 145 keV
Note: yield
at 90 o is
very small
Med Phys 35 (2008) 4308
50/47

60
Co therapy unit
Issued
June 17,
1988
Thanks to
Jerry Battista
51/47

Simulating an Eldorado6
Mora et al Med Phys 26(1999) 2494
52/47

Output variation vs expt
Med Phys 26(1999) 2494
53/47

10 & 20 MV beams from NRC linac
NRC research
accelerator,
everything is known
about it, including
incident electron
beam energy.
Ion chamber
measurements.
A systematic
problem near
surface
Sheikh-Bagheri et al Med Phys 27(2000) 2256–2266
54/47

LaRussa et al: variation of pressure
x-ray beams
• experiment = solid line
• EGSnrc = dashed line
• Calculated results generally within 0.5%.
Med Phys 34 (2007) 4690
55/47